I think, the problem with the laptop is that it has overheated. Have you noticed any strange warming on the bottom of the laptop prior to the shutdown of the laptop? If so, I think the chance for the CPU to be extremely heated is severe. Probably, there would be a need for replacement either the CPU and the thermic paste but it won't hurt if you check the power supply unit of the motherboard as well.
If you're unsure how to proceed, please go to PC repair company where you could trust the PC specialists to repair your laptop.